Of course, both men and women make beauty decisions to attract potential partners, but it is very common for women to make beauty decisions that may actually reduce their attractiveness to men, such as dyeing their eyebrows. They often do this for themselves or to achieve a certain aesthetic, without caring what men think.
Asian people don’t have “small eyes.” It’s an illusion created by a slight, average difference in palpebral fissure height, which is usually somewhat smaller in Asian populations in most anthropometric research.
So, the question becomes: Why did this trait evolve? A common answer is “to keep their eyes warm,” but this doesn’t make much sense, as we also see this trait in some African populations (e.g., the Khoisan).
A better hypothesis is that this was an adaptation to reduce glare, as this would apply to most of the environments where this trait is common. For instance, it’s plausible this trait evolved in northeast Asia, where snowy and open environments with glare were common, and then it spread throughout the continent from there.
But it’s an open question: What do you think of this hypothesis?